Blind demixing with multiple brain graphs. fig:brain depicts the rate of successful recovery using up to five different brain graphs corresponding to different people. The graphs belong to a dataset of six undirected graphs of the human brain, consisting of \(\text{N}=66\)  regions of interest (ROI) and edges given by the density of anatomical connections between regions [1]}. The level of activity of each ROI in a brain graph can be represented by a graph signal \(\mathbf {x}_\text{i}\) , thus, successive applications of \(\mathbf {S}_\text{i}\)  model a linear evolution of the brain activity pattern. Under the hypothesis that we observe a sum of linear combinations (filtered signals) resulting from diffusing originally sparse brain signals, then blind demixing jointly estimates which regions of the brains were originally active, the activity in these regions, and the diffusing coefficients \(\mathbf {h}_\text{i}\)  of the linear combinations. In this experiment, \(\text{L}\)  and \(\text{R}\)  vary, \(\text{S}=1\) , and the GSO \(\mathbf {S}_\text{i}\)  is chosen to be the Laplacian matrix. The results show that demixing is indeed feasible, although the performance decreases quickly as \(\text{R}\)  increase. This is not surprising since the brain graphs at hand exhibit strong similarities. On the other hand, for a fixed value of \(\text{R}\)  it is interesting that the performance increases with \(\text{L}\)  growing from 2 to 4, and it starts to drop afterwards. This reveals a trade-off between the number of parameters to estimate (increasing with \(\text{L}\) ) and the amount of information of \(\mathbf {x}_{\text{i}}\)  in \(\mathbf {y}\)  (which increases with the successive diffusions).
